APPENDICES

APPENDIX - A

DATA FOR IEEE-30 BUS TEST SYSTEM

The one line diagram of an IEEE-30 bus system is shown in Fig. A.I. 'The

System data is taken from references [I471 (1491. The line data. bus data and load

flow results are given in Tables A.land A.2, respectively. The generator cost and

emission coefficients, transformer tap setting, shunt capacitor data are provided in

Table A.3, A.4 and A.5, respectively. The B-loss coefficients mauix of the system is

given in Table .4.6. The data is on I00 MVA base.

Fig. A.1. One line diagrnrn

Table A.2. Bus data and Load tlow mults

i Bus 1 No.

1

--

3

4

5

6

7

8 1 1 - -

Bus Voltage

Magnitude (P.U')

1.06

1,045

1,000

1.060

1.010

1.0""

1,000

1,010

1 .000

Phase Angle

(degrees)

O.OoO

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

Generation

0 I

1 1

! 12

1 13

Real Power (p.u.)

1.3848

0.4

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.00"

0.000

0.000

0.000

0.000

1,000

1.082

1 .000

1,071

Reactive Power

(p.u.)

-0.0279

0.5

0.000

0.000

0.37

0.000

0.000

0.373

0.000

0.000

0.162

0.000

@I06

0.000

Load

0.058

0.000

0.1 12

0.000

--

Real Power (p.u.)

0.000

0.217

0.024

0.076

0.942

0.000

- 0.228

Reactive Power Limits

Reactive Power (p .~ . )

0.000 -.

0.127

0.012

0.01 6

- 0.19

0.000

. -. 0.109

Qlim

(P-U-) - -

4 . 2

0.062 0.016 - -

- 0.3

0.000

-. 0.02

0.000

0.075

- 0.000

QN, ( p . ~ . )

-

0.6

0.3

0.000

-

4 .10

-

4 . 1 5

-

- -

4.15

-

-

0.40

-

0.45

- -

0.625

-

- -

-0.1.5

-

0.50

Table A.3. Generator cost and Eminsion coe~cients

Table A4. Transformer tap setting data

Table A.5. Shunt capacitor data

Table A.6. Generalized loss coeff~cients

B,", = [0.000014]

APPENDIX - B

DATA FOR 6 UNIT TEST SYSTEM

The system contains six thermal units. 26 buses, and 46 trimmission lines

1421. The load demand is 1263 MW. The cost coefficients o f 6 unit test system arc

given in Tables B.1. The ramp rate limits o f corresponding generating units are given

in Table B.2. The generalized B loss coeficients for the system are shown Table A.3.

The system data is on 100 MVA base.

Table B.I. Generating Unit Capacity and Coemcienb

p,rnln pim.= a( Unit

(MW) (MW) ( S I M W ~ ~ )

Table B.Z. Ramp Rate Limits and Prohibited Operating Zones

Table B.3. Generalized loss cocflicienta

APPENDIX - C

DATA FOR l I U N l T TEST SYSTEM

The 15-unit test system contains 15 thermal units whose characleristics are

given in Tables C.1, C.2, respectively. The generalized loss cmfiicients an given

Table C.3. The system data is taken from reference 1421.

Table C.1. Generating unit with ramp rate limits

Table C.2. Prohibited operating zones of generating units

Table C.3. Generalized loss coeflicients

Unit

I1 (1114 01K112 O M 0 1 4 INX>I 4 1 X X 1 3 4 WL)I 4 1 OX111 4 IKYI I 4 1 WX13 0 LXXI5 4 I K Y l 1 - l l I l K J Z (I I Y K U 0 ( X U 3 4 INKI? 0 W112 0 i K l 1 3 O l X I I 1 (I INXNI -11 - 0 WW2 11 I X I N I II IXXI I 4 l lXN13 4 1 (XXU - 0 IXXM -0 11KXi 11 I I X Y I I I X I I I I 4 I I I X I 2 00(1(11 O W M l 0 0 0 1 0 4 IMII 41NJ13 4 l I X X N 4 I l Y X I I I I I K X W U W I H 4 I X 1 1 2 I I 1 X ) I l I I I X X X I 4 M I 3 5 0111 11 4 l X 1 2 Y 4 i K K l l 4 UXl5 4 ) W11l 0 1x134 -1, l X W 4 M I 4 ll 1x11 I I I ( U X 0 0 0 0 2 9 0 0 0 3 2 -(I IN11 I - 0 (11XI I I L X I I I 0 INXI1 4 1 IN126 -11 1x11) .IIIIX>~ -11 (mil II w i 7 I ~ ( X ~ I (1 in114 II (XNI~ I I I X I I ~ n INIIU a I ~ I I ~ o 1 m 1 1 -1) I r x c 4 1 INXC u l x l n 4 1 ( u r n 4 MII UIXKKI 4 IXIN 4 1 IXKM o(1114 (I 1 ~ 1 1 0 II IYYUI -(I INXK a r m 5 4 n n l w ~ IX I I I 4 1 ( r w n 1~x1: 41 rx,11 e l x n l 4 M X I I 111KK11 - 0 (XKII 11 IN11 1 4 1 (XKl3 4 1 (KKK1 (I 1X)I 5 11 l X l 1 7 11 I X I l h I I I X X W -11 ( X X h 11 11N17 4, 11XXl 4 l I X N l ? 4 1 IN118 .I, *XI) 11 IXHII o am^ a I X ~ S I ~ 4 1 IXII? .ii II a l l 1 0 0 1 6 ~ o msl IIIXI~V 4 1 IXI:I 11 IXII~ IIIXYII o IXUK 4 1 ( ~ 1 7 8

1 4 iKX13 - 0 M I 2 -11 WXIX 11 1112'4 -1, I K l l l l 4 IXXIS 0 (XI15 0 W I X : O O I W 1101 I h 4 1 X i 2 1 4, IN125 0 IXU11 - 0 IN111 4 1 (1172 -1, lXX13 -11 (KYN -11 W113 I1 11132 - 0 (XI13 - 0 IXXIX I ! IXHIV 0 1Nl7V 0 111 1 0 OI IZIKI 4 1 IN127 4 ) 11114 I,lXNW 4 I X I I I 4 I l X I W I - 0 l K K l 3 - 0 W X N - 0 0 0 1 7 4 I I N l I I I ) I M 1 7 1 l i X ) I I 4 IKXIS -0(1123 - 0 0 0 2 1 4 1 X 1 2 1 I I I 1 1 4 1 I I I X X I I I I I N X U 4I lY138 O l l l h X , n NXI? -11 WXI -OIKNX~ 41 IKXN> 4 1 ~ ~ : 4 WXII (I [ r u n 4 1 1 s % 4 1 ~ 2 s 11rn14 OIXXII IIINW a t x x ) l 11 c w r v 111rn8 IIMM O(KH)I .0(1125 (IIYUII -1111~12 -O~KUI: i ~ ( x ~ m i (IINNII IIIYLI~ o i x n r , ~ I M K U - i i i r x i t 1,111 111 ~IIIIIII OIKIZX UIXK13 11(Kl1<1 (101 1 I < i W \ l -U<1114 -OINI I7 .(I IXXl2 I l l X X l 5 d l X l 1 2 4 ) l X I I I I)<Xl1W -1IIXXN 4 1 I 1 I I I I B W X a W W 4

-11 IXKI I - 0 lXK12 41 (XI28 4 j l X l 2 h 4 ) IKX13 11 IXW3 4 I l X X l B 4 1 lY178 -011172 4 1 IXIWII O O l 0 8 II(112X O(X12X -1) I I U 4 O 1 2 1 3

Prohibited Zones (MW) 1

APPENDIX - D

DATA FOR TAIPOWER 40-UNIT SYSTEM

The system data 1s taken from reference [50] whose characteristics am glven

In Table D.1. The data is on 100 MVA base.

Table D.1. Generating units coeff~cients with ramp rate limits

APPENDIX - E

LINE VOLTAGE STABILITY INDEX

The important aspect of voltage stability assessment is lo find the distance

(MW/MVAR/MVA) to maxlmum loadabtllty point from the present operating point

[115]. Line voltage stahil~ty index 1s used to get accurately the proximity of the

operating point to voltage collapse point by the mdcx glven as follows. Let us

consider a single line of an lnterconnccted network. where the lines are connected

through a grid network. Any of the lines from that network can be considered to have

the following parameters as shown In Fig. E. 1. Utlliz~ng the concept of power flow In

the line and analyzing with '11' model representation, the real and reactlve power llow

equations in terms of transmiss~on llne constants are formulated

Fig. E.1. One line diagram of a typical transmission system

Loads are more often expressed In terms of real (WattsIKW) and reactlve

(VArsKVAr) power. Therefore, 11 1s convenient to deal with transmission llne

equation in the form of send~ng and receiving end complex power and voltage.

Let us treat receiving end voltage as a reference phasor (VR = IVRILO) and let

the sending end voltage lead it by an angle S(Vs = IVslL6). Transrnlssion lines are

normally operated with a balanced 3 phase load. The analysis can be therefore

performed on per phase basis.

The complex power leaving the sending- end and entering the receiving end of

the transmission line can be expressed on per phase basis [154], as

A transmission llne on a per phase basis, can be regarded as a two-pon

network, where in the sendlng end voltage, Vs and current. IS are related to the

receiving end voltage, VK and current. IR through ABCD constants [I541 as

Receiving and sending end currents can hc expressed In terms ofreceivlng and

scndlng end voltagcs [ I 54) as

1 = I v . A V B S B Y

(E 3)

Let A, B, D the transmission l ~ n e constants [I 541 he wrltten as

A = I A l i a l . R - IBILPI. 1) - ID1 LUI (Since A =D)

Therefore we can write,

Substituting for In in equation (E.1) we get,

If equation (E.8) is expressed In real and rlnaglnarv parts, we can write the real and

reactive powers at the receiving end [I 541 as.

where A La 1 and B LP I are the transnilsston l ~ n e constants

For the usual n-model, the transmlsslon l ~ n e constants may be written as follows

If the length of the line is medium, then

Z is the total series impedance of ltne,

Y is the total line charging susceptance.

If it is a long transmission line, then

Z'Y' A=]+--

2

B = Z' where

(E. 12)

(E. 13)

y IS propagation constant and 1 is the length o f ~ a n s r n ~ s s ~ o n llne

The formulae for the receiving end real and reactive powers can he formulated as follows [ I 541

These can be rewritten as,

(E. I 8)

E I E I E ~ ' A I S l n ( p , -a,)= L - L s ~ n ( p , - 8 ) Q , +--- (E. 19)

IBI IB I Then by el~rninatlng 6. by squanng and adding the two equations, we obtain

the locus of PH against QR to be a c~rcle with given values o f A and B and for assumed

values of ER and jEs/ to be [I 541 as follows.

If kth bus is the sending end and m" bus is the receiving end and expanding the

above equation we get as follows,

The above equation should have the real roots for V,,, for the system to be

stable. Hence the following condition should bc satisfied[ 1541

where, LS, is termed as voltage stability index of the line P, and Q, are the real and

reactive power rece~ved at the receiving end rn, ALal and BLP are the transmission

11ne constants, Vk and V, are the voltages at the sending end bus k and receiving end

bus m.

At or near the collapse point, voltage stabil~ty index of one or more line

approach to unity. This method is used to assess the voltage stability.

APPENDIX - F

STANDARD - 5 BUS SYSTEM

The Standard 5 bus system is shown in Fig. F.I. The System data is taken

from reference [154]. The line data and bus data are given in Tables F.1. F.2,

respectively. The data is on I00 MVA base.

Fig. F.I. One line diagrnm

Table F.1. Line dnta

Table F.2. Bus Data

APPENDM - G

DATA FOR IEEE-14 BUS TEST SYSTEM

The one line diagram of an IEEE-14 bus system is shown in Fig. G.1. The

System data is taken from reference [147]. The line data, bus data and load flow

results are given in Tables G.1. and G.2, respectively. The data is on 100 MVA base.

C Spchrmxnn Comnprm*ors h G Gcnt~ators

Three Wmdi . Transformer Equivalent

-r9 e Fig. G.1. One line diagram

Table G.1. Line data

1 I I I Line lmocdanec I Half Line Line 1

I 1 2 0.01938 0.05917 0.02640

F~~~ Bus

TO Bus

Charging s~~~~~~~~~

(P.u.)

Resistance @-u)

Reactance (P.u)

Tabk G.2. Bus data and load flow results

Bus No.

1

2

3

4

5

6

7

8

9 -

10

11

12

13 -

14

Bus Voltage

Ma'nitude (P.U)

1.060

1.045

1.010

1 .OW

1.000

1.070

1.000

1.090

1.000

1.000

1.000

1.000

1.000

1.000

Generation

1:;: (degrees)

O.O0O

O.OoO

O.OOO

O.OoO

O.OOO

O.OoO

0.000

O.OOO

~

O.OOO

O.OOO

O-OoO

O.OoO

O.OO0

Real Power (p.u)

2.324

0.400

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

Reactive power

( p . ~ )

-0.169

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

Load

R u l Power (p.u)

0.000

0.217

0.942

0.478

0.076

0.1 12

O.O(H)

0.000

0.295

0.090

0.035

0.061

0.135

0.149

Reactive Power

Reactive power (p.u)

0.000

0.127

0.191

0.039

0.016

0.075 . .

0.000

0.000

0.166

0.058

0.018

0.016

0.058

0.050

Qm,m

(Pu)

-

-

- -

-0.06

~.- .- -

4.0h

-

-

-

-

-

Limits

Qmm,

(Ku)

-

0.50

0.40

-

KT'' --

0.24

-

-

-

-

-

Table G 3 . Transformer tap ~ n i a g data

Table G.4. Shunt capacitor data

TapSctting ' Value (p.u.)

0.978

0.969

0.932

From Bus

4

4

5

To Bus

7

9

6

APPENDIX - H

DATA FOR AN IEEE-57 BUS TEST SYSTEM

The System data is taken h m reference [147]. The line data bus data and

load flow results for an 1EEE-57 bus system given in Tables H.1 and H.2.

respectively. The transformer tap setting and shunt capacitor data are provided in

Table H.3 and H.4, respectively. The data is on 100 MVA base.

Table H.1. Line data

Table H.Z. Bus data and load flow results

Table H3. Transformer tap setting data

Table H.4. Shunt capacitor data

From Bus

4 I 18 1 0.97

To Bus

Tap Setting Value (P.u.)

APPENDIX - I

DATA FOR INDIAN UTILITY-NTPS23 BUS SYSTEM

The Indian utility Neyveli Thermal Power Station (NTPS)-23 bus test system

is shown in Figure J.1 .The sites of buses, line data, bus data, me given in Tables 1.1.

1.2 and 1.3. respectively. A 100 MVA. 400 KV base is chosen.

Fig. 1.1. One line diagram

Tabk 1.1. Sitar and location of different buses

I I

12

13

14

15

16

17

18

19

20

2 1

22

23

TV MALAl (230 KV)

CUDDALORE (230 KV)

MDS (400 KV)

SLMI (400 KV)

SLlvI2 (400 KV)

TRY 1 (400 KV)

TRY2 (400 KV)

ST1 -ST3 (110KV)

D.KURUCH1 ( I I 0 KV)

VPM 1 & 2 ( 1 1 0 K V )

VDU (1 10 KV)

P-PDY (1 10 KV)

TVR ( I 10 KV)

Thiruvannamalai

Cuddalore

Madras

Salem 1 -- . - .

Salem2 .. . - . . -- -.

'I'richy I .- --- --

1-richy2

Station ~uxillarie;

Deva Kuruchi - -

Villupuram

Vadakuthu

Pondicherry

Thiruvarur I

Table 13. Line data

Tabk 1.3. Bus data

APPENDIX - J

DATA FOR INDIAN UTILITY-PUDUCHERRY- 17 BUS SYSTEM

The Indian utility-Pondicherry-I7 bus test system is shown in Fig. J.1. The

line data bus data, are given in Tables J.l.and J.2.. respectively. A 100 MVA.

11 0 KV base is chosen.

Fig. J.1. One line diagram

Table J.1. Line Data

Half Line Charging

L I I I I I

Table J.2. Bus data - - - - - - -- -

-- -

L.oaJ - - --I Reactive

Power 1